<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>2116100 - Disclosure - Related Party Disclosures and Transactions</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>D2013Q2YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000051548</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2012-12-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-05-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="May 31, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_TextBlockAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Text Block [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_RelatedPartyTransactionsDisclosureTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-family:Times New Roman;font-size:10pt;"&gt;&lt;div style="line-height:120%;padding-top:18px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;Related Party Disclosures and Transactions&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:6px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;All of the racing events that take place during the Company&amp;#8217;s fiscal year are sanctioned by various racing organizations such as the American Historic Racing Motorcycle Association, the American Motorcyclist Association, the Automobile Racing Club of America, the American Sportbike Racing Association &amp;#8212; Championship Cup Series, the Federation Internationale de L&amp;#8217;Automobile, the Federation Internationale Motocycliste, Grand American Road Racing Association (&amp;#8220;Grand American&amp;#8221;), Historic Sportscar Racing, IZOD IndyCar Series, National Association for Stock Car Auto Racing (&amp;#8220;NASCAR&amp;#8221;), National Hot Rod Association, the Porsche Club of America, the Sports Car Club of America, the Sportscar Vintage Racing Association, the United States Auto Club and the World Karting Association. NASCAR, which sanctions many of the Company&amp;#8217;s principal racing events, is a member of the France Family Group which controls approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;72.0 percent&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; of the combined voting power of the outstanding stock of the Company, as of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;November&amp;#160;30, 2012&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, and some members of which serve as directors and officers of the Company. Standard NASCAR sanction agreements require racetrack operators to pay sanction fees and prize and point fund monies for each sanctioned event conducted. The prize and point fund monies are distributed by NASCAR to participants in the events. Prize and point fund monies paid by the Company to NASCAR from continuing operations for disbursement to competitors, which are exclusive of NASCAR sanction fees, totaled approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$40.4 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$41.5&amp;#160;million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; for the three months ended &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;May&amp;#160;31, 2012&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, respectively, and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$62.7 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$64.7&amp;#160;million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; for the &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;six&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; months ended &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;May&amp;#160;31, 2012&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, respectively.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:6px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Under current agreements, NASCAR contracts directly with certain network providers for television rights to the entire NASCAR Sprint Cup, Nationwide and Camping World Truck series schedules. Under the terms of this arrangement, NASCAR retains &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;10.0 percent&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; of the gross broadcast rights fees allocated to each NASCAR Sprint Cup, Nationwide and Camping World Truck series event as a component of its sanction fees. The promoter records &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;90.0 percent&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; of the gross broadcast rights fees as revenue and then records &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;25.0 percent&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; of the gross broadcast rights fees as part of its awards to the competitors. Ultimately, the promoter retains &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;65.0 percent&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; of the net cash proceeds from the gross broadcast rights fees allocated to the event. The Company&amp;#8217;s television broadcast and ancillary rights fees from continuing operations received from NASCAR for the NASCAR Sprint Cup, Nationwide, and Camping World Truck series events conducted at its wholly owned facilities, and recorded as part of motorsports related revenue, were approximately  &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$89.6&amp;#160;million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$92.3&amp;#160;million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; for the three months ended &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;May&amp;#160;31, 2012&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, respectively, and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$143.3 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$149.7 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; for the &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;six&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; months ended &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;May&amp;#160;31, 2012&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, respectively.&lt;/font&gt;&lt;/div&gt;&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for related party transactions. Examples of related party transactions include transactions between (a) a parent company and its subsidiary; (b) subsidiaries of a common parent; (c) and entity and its principal owners; and (d) affiliates.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 850

 -SubTopic 10

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6457730&amp;loc=d3e39603-107864



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 850

 -SubTopic 10

 -Section 50

 -Paragraph 4

 -URI http://asc.fasb.org/extlink&amp;oid=6457730&amp;loc=d3e39622-107864



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 850

 -SubTopic 10

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6457730&amp;loc=d3e39549-107864



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 04

 -Paragraph b

 -Article 3A



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 235

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.4-08.(k))

 -URI http://asc.fasb.org/extlink&amp;oid=6881521&amp;loc=d3e23780-122690



Reference 6: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 08

 -Paragraph k

 -Article 4



Reference 7: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 850

 -SubTopic 10

 -Section 50

 -Paragraph 6

 -URI http://asc.fasb.org/extlink&amp;oid=6457730&amp;loc=d3e39691-107864



Reference 8: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 850

 -SubTopic 10

 -Section 50

 -Paragraph 5

 -URI http://asc.fasb.org/extlink&amp;oid=6457730&amp;loc=d3e39678-107864



Reference 9: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 57

 -Paragraph 1-4

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Related Party Disclosures and Transactions</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Related Party Disclosures and Transactions</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.internationalspeedwaycorporation.com/role/RelatedPartyDisclosuresAndTransactions</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
